Appendix 1 Formulas of CFROI Starting from the following formula GI ¼ GCFa njCFROI þ SV 1 þ CFROI ð Þ n we can demonstrate how the following alternative formulation of the CFROI can be derived, if we assume in the calculation of economic depreciation a discount rate k = CFROI = r CFROI ¼ Gross Cash Flow Economic Depreciation ð Þ=Gross Investment Stating that: ED ¼ economic depreciation ¼ GL SV ð Þ s njr where s njr ¼ð1 þ rÞ n 1 ½ =r is the ﬁnal value of an n-period annuity with interest rate r multiplying each member of the above equation by (1+r) n and therefore subtracting from each member GI, we can rewrite the relationship as follows: GI ð1 þ rÞ n 1 ½ ¼ GCF s njr ED s njr : Being ð1 þ rÞ n 1 ½ ¼ r s njr and a njr ¼ s njr ð1 þ rÞ n ; we can get r GI ¼ GCF ED therefore r ¼ GCF ED ð Þ=GI quod erat demonstrandum ð Þ D. Venanzi, Financial Performance Measures and Value Creation: The State of the Art, SpringerBriefs in Business, DOI: 10.1007/978-88-470-2451-9, Ó The Author(s) 2012 71

Appendix 1 Formulas of CFROI - link.springer.com978-88-470-2451-9/1.pdf · Appendix 1 Formulas of CFROI Starting from the following formula GI ¼ GCFa njCFROI þ SV ðÞ1 þ CFROI

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Appendix 1Formulas of CFROI

Starting from the following formula

GI ¼ GCFanjCFROI þSV

1þ CFROIð Þn

we can demonstrate how the following alternative formulation of the CFROI canbe derived, if we assume in the calculation of economic depreciation a discountrate k = CFROI = r

CFROI ¼ Gross Cash Flow� Economic Depreciationð Þ=Gross Investment

Stating that:

ED ¼ economic depreciation ¼ GL� SVð Þ � snjr

where snjr ¼ ð1þ rÞn � 1½ �=r is the final value of an n-period annuity with interestrate r

multiplying each member of the above equation by (1+r)n and thereforesubtracting from each member GI, we can rewrite the relationship as follows:

GI ð1þ rÞn � 1½ � ¼ GCF � snjr � ED� snjr:

Being ð1þ rÞn � 1½ � ¼ r � snjr and anjr ¼ snjr � ð1þ rÞn; we can get

r � GI ¼ GCF � ED therefore r ¼ GCF � EDð Þ=GI quod erat demonstrandumð Þ

D. Venanzi, Financial Performance Measures and Value Creation: The State of the Art,SpringerBriefs in Business, DOI: 10.1007/978-88-470-2451-9,� The Author(s) 2012

Page 2: Appendix 1 Formulas of CFROI - link.springer.com978-88-470-2451-9/1.pdf · Appendix 1 Formulas of CFROI Starting from the following formula GI ¼ GCFa njCFROI þ SV ðÞ1 þ CFROI

Appendix 2Excess Investor Return in Terms of EVA

According to O’Byrne (1997), we can express the excess investor return in year 1as follows: MV1 + FCF1 - (1 + k)MV0.

Expressing FCF (free cash flow) and MV (market value) in terms of EVA, wecan write:

MV0 ¼ cap0 þ EVA0=k þ ðð1þ kÞ=kÞX1

i¼1

x0DEVAi=ð1þ kÞi

FCFi ¼ NOPAT1 � Dcap1 ¼ EVAi þ kcap0 � Dcap1

MV1 ¼ cap1 þ EVA1=k þ ðð1þ kÞ=kÞX1

i¼2

x1DEVAi=ð1þ kÞi�1

where x0DEVAi and x1DEVAi are the investors’s expectations, at the end of year 0and 1, of EVA improvement in year i.

Collecting similar terms and simplifying, we obtain the following relation ofthe excess return in year 1:

ðð1þ kÞ=kÞð EVA1 � EVA0ð Þ � x0DEVA1Þ þ ðð1þ kÞ=kÞX1

i¼2

ðx1DEVAi � x0DEVAiÞ=ð1þ kÞi�1

Generalizing, we can express the n year excess return as follows:

ðð1þ kÞ=kÞð EVAn � EVAn�1ð Þ � x0DEVAnÞ þ ðð1þ kÞ=kÞX1

i¼nþ1

ðxnDEVAi � x0DEVAiÞ=ð1þ kÞi�n

D. Venanzi, Financial Performance Measures and Value Creation: The State of the Art,SpringerBriefs in Business, DOI: 10.1007/978-88-470-2451-9,� The Author(s) 2012